Alphabeta MathInduced Subgraphs and Hereditary Graph Classes — Examples
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✓ 12 results · all verified · 0 also independently AI-judged
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1 · Prerequisites
Combinatorics
Real Analysis
2 · Logical flowchart
3 · Items
Counterexample
K₃ contains P₃ as a subgraph but not as an induced subgraph
Example
ind_K₂(G)=2|E(G)| under the induced-embedding convention
Example
Complete graphs form the hereditary class with forbidden basis {K̄₂}
Example
Edgeless graphs form the hereditary class with forbidden basis {K₂}
Example
A graph is P₃-free if and only if every connected component is complete
Counterexample
The class of connected graphs is not hereditary
Counterexample
The class of regular graphs is not hereditary
Example
P₄ is both connected and anticonnected
Example
Complete, anticomplete and mixed vertex-set pairs in P₄
False statement
Every hereditary graph class has a finite forbidden induced-subgraph basis
False statement
Every hereditary graph class is closed under taking arbitrary subgraphs
Example